Abstract
A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice Ω(η), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets.
| Original language | English |
|---|---|
| Pages (from-to) | 1-28 |
| Number of pages | 28 |
| Journal | Order |
| DOIs | |
| Publication status | Accepted/In press - Nov 21 2016 |
Keywords
- Algebraic lattice
- Convex geometry
- Lattices of relatively convex sets
- Lattices of suborders
- Lattices of subsemilattices
- Multi-chains
- Order-scattered poset
- Topologically scattered lattice
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics